Finite Group Databasebeta

← #93186

Subgroups — #93186

Order 512.

380 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#8555C211yesmaximal, characteristic
2#8555C211yesmaximal, characteristic
3#8550C211yesmaximal, characteristic
4C22×C22⋊Q8C2211yescharacteristic
5#1821—21no—
6#1821C412yes—
7#1784C412yes—
8#1463—21no—
9#1463—21no—
10#1463—21no—
11#1462—21no—
12#1462—21no—
13#1462C412yes—
14C23×Q8C2×C411yescharacteristic
15C24×C4Q811yescharacteristic
16C2×C22⋊Q8—42no—
17C2×C22⋊Q8—42no—
18C2×C22⋊Q8—42no—
19C22×C4⋊C4C2×C411yescharacteristic
20C22×C4⋊C4D411yescharacteristic
21C22×C4⋊C4D411yescharacteristic
22C22×C22⋊C4C2×C411yescharacteristic
23C22×C22⋊C4D411yescharacteristic
24C2×#101—42no—
25#407—22no—
26#407—22no—
27#407—22no—
28#343—42no—
29#343—42no—
30#324—42no—
31#324—42no—
32#324—42no—
33#323—42no—
34#323—42no—
35#323—42no—
36C25C4⋊C411yescharacteristic
37C22×Q8—22no—
38C22×Q8—41no—
39C22×Q8—41no—
40C22×Q8—82no—
41C23×C4—41no—
42C23×C4—41no—
43C23×C4—41no—
44C23×C4—82no—
45C23×C4C4211yescharacteristic
46C23×C4C22⋊C411yescharacteristic
47C23×C4C22⋊C411yescharacteristic
48C23×C4C22⋊C411yescharacteristic
49C23×C4C4⋊C411yescharacteristic
50C23×C4C4⋊C411yescharacteristic
51C2×M16—42no—
52C2×M16—42no—
53C2×M16—42no—
54C22⋊Q8—416no—
55C2×C4⋊C4—22no—
56C2×C4⋊C4—22no—
57C2×C4⋊C4—22no—
58C2×C4⋊C4—22no—
59C2×C4⋊C4—22no—
60C2×C4⋊C4—41no—
61C2×C4⋊C4—41no—
62C2×C4⋊C4—41no—
63C2×C4⋊C4—41no—
64C2×C22⋊C4—22no—
65C2×C22⋊C4—22no—
66C2×C22⋊C4—22no—
67C2×C22⋊C4—41no—
68C2×C22⋊C4—41no—
69C2×C22⋊C4—41no—
70#101—84no—
71C22⋊C8—42no—
72C22⋊C8—42no—
73C22⋊C8—42no—
74C22⋊C8—42no—
75C22⋊C8—42no—
76C22⋊C8—42no—
77C24—21no—
78C24—21no—
79C24—21no—
80C24—42no—
81C24—81no—
82C24—81no—
83C24#9511yescharacteristic
84C2×Q8—44no—
85C2×Q8—44no—
86C2×Q8—82no—
87C2×Q8—82no—
88C2×Q8—82no—
89C2×Q8—82no—
90C2×Q8—82no—
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—21no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—21no—
99C22×C4—21no—
100C22×C4—21no—
101C22×C4—21no—
102C22×C4—21no—
103C22×C4—21no—
104C22×C4—21no—
105C22×C4—21no—
106C22×C4—42no—
107C22×C4—44no—
108C22×C4—82no—
109C22×C4—82no—
110C22×C4—82no—
111C22×C4—81no—
112C22×C4—81no—
113C22×C4—81no—
114C22×C4—81no—
115C22×C4—82no—
116C22×C4—82no—
117C22×C4—82no—
118C22×C4—81no—
119C22×C4#9912yes—
120C22×C4#9912yes—
121C22×C4#9912yes—
122M16—84no—
123M16—84no—
124M16—84no—
125C2×C8—82no—
126C2×C8—82no—
127C2×C8—82no—
128C4⋊C4—44no—
129C4⋊C4—44no—
130C4⋊C4—44no—
131C22⋊C4—44no—
132C22⋊C4—44no—
133C23—22no—
134C23—22no—
135C23—22no—
136C23—41no—
137C23—41no—
138C23—41no—
139C23—41no—
140C23—41no—
141C23—41no—
142C23—41no—
143C23—81no—
144C23—81no—
145C23—81no—
146C23—81no—
147C23—81no—
148C23—81no—
149C23—88no—
150C23#34211yescharacteristic
151C23#34211yescharacteristic
152C23#34211yescharacteristic
153Q8—88no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—81no—
172C2×C4—81no—
173C2×C4—81no—
174C2×C4—81no—
175C2×C4—81no—
176C2×C4—88no—
177C2×C4—81no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4—81no—
181C2×C4—81no—
182C8—162no—
183C8—162no—
184C8—162no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—44no—
195C22—42no—
196C22—82no—
197C22—82no—
198C22—82no—
199C22—82no—
200C22—82no—
201C22—82no—
202C22—81no—
203C22—81no—
204C22#130411yescharacteristic
205C4—42no—
206C4—42no—
207C4—42no—
208C4—42no—
209C4—81no—
210C4—81no—
211C2—41no—
212C2—41no—
213C2—41no—
214C2—82no—
215C2#731111yescharacteristic
216C2#731311yescharacteristic
217C2#731511yescharacteristic
subgroupG/H
center, socleC22#1304
commutatorC23×C4C42
Frattini, cosocleC22×C22⋊Q8C22
prime radicalC25C4⋊C4
LCSG ▷ C23×C4 ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊Q8 ◁ G
LECSG ▷ C22×C22⋊Q8 ▷ C24 ▷ C22 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#85552
#85502